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1.6 Trigonometric Functions

1.6 Trigonometric Functions. Graphs of Trigonometric Functions. When we graph trigonometric functions in the coordinate plane, we usually denote the independent variable (radians) by x instead of θ. Sine is an odd function because:. Even and Odd Trig Functions:.

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1.6 Trigonometric Functions

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  1. 1.6 Trigonometric Functions

  2. Graphs of Trigonometric Functions • When we graph trigonometric functions in the coordinate plane, we usually denote the independent variable (radians) by x instead of θ .

  3. Sine is an odd function because: Even and Odd Trig Functions: “Odd” functions behave like polynomials with odd exponents, in that when you change the sign of x, the sign of the y value also changes. Cosecant, tangent and cotangent are also odd, because their formulas contain the sine function. Odd functions have origin symmetry.

  4. Even and Odd Trigonometric Functions • The graphs of cos x and sec x are even functions because their graphs are symmetric about the y-axis. • The graphs of sin x, csc x, tan x and cot x are odd functions.

  5. Example Even and Odd Trigonometric Functions

  6. Trig Identities

  7. Angle Convention

  8. Arc Length - Area

  9. is a stretch. is a shrink. The rules for shifting, stretching, shrinking, and reflecting the graph of a function apply to trigonometric functions. Vertical stretch or shrink; reflection about x-axis Vertical shift Positive d moves up. Horizontal shift Horizontal stretch or shrink; reflection about y-axis Positive c moves left. The horizontal changes happen in the opposite direction to what you might expect.

  10. is the amplitude. is the period. B A C D When we apply these rules to sine and cosine, we use some different terms. Vertical shift Horizontal shift

  11. INVERSE TRIG FUNCTIONS

  12. Inverse Trigonometric Functions

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